scholarly journals Solutions of the Multivariate Inverse Frobenius–Perron Problem

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 838
Author(s):  
Colin Fox ◽  
Li-Jen Hsiao ◽  
Jeong-Eun (Kate) Lee
Keyword(s):  
Uniform Distribution ◽  
Two Dimensions ◽  
Target Distribution ◽  
One Dimensional ◽  
All Solutions

We address the inverse Frobenius–Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

The Structure of Emotional Response: 1984 Presidential Candidates

1988 ◽  
Vol 82 (3) ◽  
pp. 737-761 ◽  
Author(s):  
George E. Marcus
Keyword(s):  
Emotional Response ◽  
Two Dimensions ◽  
Negative Emotionality ◽  
One Dimensional ◽  
Presidential Candidates ◽  
The Past ◽  
Emotional Appraisal ◽  
Psychological Models ◽  
Dimensional Models ◽  
Feeling Thermometer

Over the past two decades psychological models of affect have changed from valence (one-dimensional) models to multiple-dimensional models. The most recent models, circumplex models, are two-dimensional. Feeling thermometer measures, which derive their theoretical logic from earlier (valence) models of emotional appraisal, are shown to be confounded. Underlying the variation obtained using feeling thermometer measures are two dimensions of emotional response, mastery (positive emotionality) and threat (negative emotionality). Analysis of the 1984 NES survey suggests that positive emotional response is twice as influential as negative emotional response in predicting presidential candidate vote disposition to the presidential candidates. Reliance on emotional response is shown to be uniformly influential across various strata of the electorate.Policy considerations have little direct influence on vote disposition, though policy considerations are indirectly related to vote disposition through the influence of issues on the degree of feelings of threat evoked by the candidates.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

An Instrument for One- or Two-Dimensional Tracking

1965 ◽  
Vol 21 (1) ◽  
pp. 307-312
Author(s):  
William C. Roehrig
Keyword(s):  
Low Cost ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Error Signal ◽  
One Dimensional ◽  
Constant Torque ◽  
Sinusoidal Motion ◽  
The Cross ◽  
Target Path

A rugged electro-mechanical tracking apparatus of simple, low-cost construction is described. The apparatus can be used for one-dimensional tracking by connecting only the longitudinal motor, thus forcing the target to move back and forth in either simple sinusoidal motion or according to the sum of two or three sinusoids. The relative phases of the three sinusoids can be rapidly altered, as can the amplitudes (within limits) of each of the sinusoids. The frequency of the sinusoids can be changed either independently or conjointly. By also connecting the cross-feed motor, an essentially unpredictable target path in two dimensions is obtained, and this path can be rapidly altered by changing cams, and/or frequency, amplitude, and phase of the sinusoids. Movement of the cursor is by low, constant torque lathe-type controls. The distance the cursor moves per each rotation of the controls, can be altered for either or both of the controls. A continuous error signal is generated which is directly proportional to the distance the cursor is off target in any direction.

Differences in the Heat Transfer at the Core-Reflector Boundary of the PBMR Due to the Use of Different Numerical Methods

2009 ◽  
Author(s):  
Pieter S. du Toit ◽  
Onno Ubbink
Keyword(s):  
Two Dimensions ◽  
Heat Sources ◽  
Coarse Mesh ◽  
One Dimensional ◽  
Root Cause ◽  
The Core ◽  
Modified Method ◽  
The Difference ◽  
Horizontal Slice ◽  
Mesh Cell

The PBMR (Pebble Bed Modular Reactor) is a High-Temperature Gas-cooled Reactor (HTGR) concept. One of the exercises of the PBMR benchmark of the Organization for Economic Cooperation and Development (OECD) is a steady state two-dimensional (2D) thermal-hydraulics simulation of a simplified PBMR with prescribed heat sources. Two different programs were used to model this exercise. They predicted similar core temperatures but the side reflector temperatures next to the core differed by more than 30 °C (when using a relatively coarse mesh). The underlying methods define temperatures at either vertices (VC) or at mesh cell centres (CC). A study was undertaken using one-dimensional (1D) implementations of the VC and CC methods to model a horizontal slice through the core. This study revealed the root cause of the different predictions. A modified version of the 1D CC method was developed that essentially predicts the same temperatures as the VC method. The extension of the modified method to two dimensions is under investigation. If the difference in predicted temperatures next to the core can be eliminated or reduced, then the focus can shift to other differences between the results of the two programs.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

The True Proportions of Gay's Acis and Galatea

PMLA ◽  
1965 ◽  
Vol 80 (4-Part1) ◽  
pp. 325-331
Author(s):  
Bertrand H. Bronson
Keyword(s):  
Eighteenth Century ◽  
Two Dimensions ◽  
One Dimensional ◽  
John Gay ◽  
The Arts ◽  
The One ◽  
The Mind ◽  
Theatrical Criticism

The Masque, or serenata, or pastoral opera, Acis and Galatea—in eighteenth-century printings it was indifferently categorized—has been not so much neglected as quite ignored by the biographers and critics of John Gay. In its entirety, words and music, it is a masterpiece, and the reasons for its lying unregarded, except by historians of music, deserve to be scrutinized because they signalize a recurrent failing on the part of those who write on the arts, when a work exists simultaneously in more than one medium. Only lately, in truth, has criticism begun to cope with Shakespeare himself as drama existent in and for living embodiment on a physical stage and nowhere else, not even in the mind of Coleridge. (Theatrical criticism is by habit only piecemeal commentary on separate productions.) Similarly, to set small matters beside great ones, only of late has the ballad of tradition begun to be considered as song and not as a literary or pseudo-literary genre, sufficient and self-sustaining in its text alone. And the bardic tradition of the Ugo-Slavs is teaching us much about the Homeric epics of which former generations were unaware. Signs, in fact, are here and there beginning to appear of an unwillingness to rest content with the one-dimensional conception of arts which are only half-fulfilled until they are realized in two dimensions or more. A drawing of a sculpture is not enough; a sculpture of an action is not enough; pantomime does not suffice the spoken scene; the verbal text of a musical scena will not satisfy. Nor can any of these be adequately criticized on a basis of missing dimensions.

Two Dimensional Ultrasonic Beam Distortion in the Breast: In Vivo Measurements and Effects

1992 ◽  
Vol 14 (4) ◽  
pp. 398-414 ◽  
Author(s):  
P. D. Freiburger ◽  
D. C. Sullivan ◽  
B. H. LeBlanc ◽  
S. W. Smith ◽  
G. E. Trahey
Keyword(s):  
Two Dimensions ◽  
System Response ◽  
Two Dimensional ◽  
Time Data ◽  
Phase Aberration ◽  
One Dimensional ◽  
Function Generation ◽  
Spread Function ◽  
Generation Computer

Two dimensional arrival time data was obtained for the propagation of ultrasound across the breasts of 7 female volunteers. These profiles were extracted through the use of cross-correlation measurements and a simulated annealing process that maintained phase closure while aligning the data. The phase aberration measured in two dimensions had a larger magnitude than previously reported phase aberration measured in one dimension in the breast A point spread function generation computer program was used to demonstrate the system response degrading effects of the measured phase aberration and the usefulness of current one dimensional phase aberration correction techniques. The results indicate that two dimensional correction algorithms are necessary to restore the system performance losses due to phase aberration.

A Two-Dimensional Formulation for Path-Placement in the Workcells of Planar 3-R Robots

1995 ◽  
Vol 117 (3) ◽  
pp. 479-484 ◽  
Author(s):  
N. A. Soman ◽  
J. K. Davidson
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Joint Space ◽  
Two Dimensions ◽  
Fusion Welding ◽  
Graphical Form ◽  
Tool Paths ◽  
All Solutions ◽  
Planar Robot ◽  
Systematic Formulation

A new systematic formulation is presented that determines suitable locations for a workpiece, and its associated task-motion, in the workspace of a three-hinged planar (SCARA) robotic workcell. It determines all acceptable positions for the first joint of the robot relative to the workpiece; therefore, all solutions are represented as an area in two dimensions, unlike existing methods of motion-planning that present them as a volume in a three-dimensional joint-space for the same planar robot. This simplifies the solution-space by reducing its dimension from three to two. All possible acceptable designs appear in a graphical form that can be readily visualized and directly measured in a Cartesian frame of reference in the workcell. Applications include locating workpieces with tool-paths for fusion welding and for deposition of adhesives.

The Anomalous Diffusion-limited Reaction Kinetics of a Phototrapping Reaction

1996 ◽  
Vol 464 ◽  
Author(s):  
Eric Monson ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Laser Beam ◽  
Two Dimensions ◽  
One Dimensional ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Classical Constant

AbstractA focused laser beam acts as both a “phototrap”, bleaching fluorophore molecules which diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction, A + T → T, in one and two dimensions. One dimensional diffusion-limited trapping kinetics are approached in capillaries with 10 μm diameters while two dimensional diffusion limited trapping kinetics are observed with unstirred samples having a quasi 2-D geometry. In the presence of stirring, the 2-D samplesexhibit the classical, constant trapping rate over time.

Sign in / Sign up

Export Citation Format

Share Document